It has been done, and quite successfully... here is a thread that might interest you...
http://www.myfishtank.net/forum/showthread.php?t=28882&highlight=Moved
Im very sorry for your losses.
Using tank water was a good idea, however most of the good bacteria was already in your filter...one thing to remember is when moving, the tank should be the LAST thing out of the house, and the FIRST thing set up at the new location. Leaving the fish in that bucket with a wonky heater was a big mistake. A heater and filter are of course the most important elements to success in fish keeping. So, dont go cheap when setting up a tank. If I knew there were problems with my heater, I sure wouldnt trust it to do the job in any circumstances. Well, you could look at this disaster and a huge learning experience or it was all for naught if you never use your tank again.
What you need to do, is research!! Then you CAN set up your tank, start over and be armed with the knowledge you NEED to be successful. It takes a lot of TIME, PATIENCE, and RESEARCH...are you willing to do that? If not, sell your tank.